Problem: Solve for $x$ : $4x^2 + 36x + 56 = 0$
Solution: Dividing both sides by $4$ gives: $ x^2 + {9}x + {14} = 0 $ The coefficient on the $x$ term is $9$ and the constant term is $14$ , so we need to find two numbers that add up to $9$ and multiply to $14$ The two numbers $7$ and $2$ satisfy both conditions: $ {7} + {2} = {9} $ $ {7} \times {2} = {14} $ $(x + {7}) (x + {2}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 7) (x + 2) = 0$ $x + 7 = 0$ or $x + 2 = 0$ Thus, $x = -7$ and $x = -2$ are the solutions.